How can "to teach" and "to learn" be translated to Russian?

Question

I know that there are several Russian verbs can be used to translate the English verbs "to teach", "to study", and "to learn", e.g. учить, выучить, научить, учиться, изучать, ...

However, I am a bit confused about their exact meaning and usage. Could you explain the meaning of the above verbs? How are the following expression translated into Russian?

• I am learning Russian.
• I am studying at University.
• I teach Russian.
• I teach Russian to the students.
• I teach my son how to drive a car.
• I am learning to drive a car.
• Where did you learn Russian?
• Who taught you Russian?

Please feel free to add any further examples that explain how to translate "to teach" and "to learn" into Russian, and how to correctly use the Russian verbs I have listed above.

Answer 1

Учить: to be studying something OR to be teaching someone.

Выучить: to learn something in full (you have completed your learning) OR to get someone learn something (you have taught someone).

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Изучать: to be studying something. Never used for "to be teaching".

Изучить: to learn something in full (you have completed your learning).

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Обучать: to be teaching someone. Never used for "to be studying".

Обучить: to get someone learn something (you have completed your teaching).

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Subtle differences between выучить and изучить:

• выучить may be used to say you learnt something by rote (although not necessarily), whereas изучить always means you actually understood it.
• (a consequence of the previous bullet): изучить always impiles thought and analysis of some sort. Because of that, you never say изучить стих, you must say выучить стих (to memorise a verse). Well, you can actually say изучить стих, but that would mean you performed a linguistic analysis of the verse, which does not imply you now know the verse by heart.

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Subtle differences between учить and обучать:

• Учить is less formal and can refer to more situations. If a person in the streets shows you how to use an ATM that has Russian interface, that's учить. Nethertheless, it may also refer to students in school.
• Обучать is more formal and generally refers to a specifically arranged teaching. You expect to see this word in a report teacher submits to school principal. However, relation to an educational institution is not required, you can say обучать instead of учить to accentuate the act of teaching was not random and/or took some time.

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How to tell apart the two different meanings of учить:

• When referring to learning, the question is 'what' (учить что?).
  When referring to teaching, the question is 'whom' (учить кого?)
• Therefore, if you want to say that you are studying a person, you must use the single-meaning form, изучать, to avoid confusion:
  

  Я учил его -> I taught him (and never I learned him)
  Я изучал его -> I studied him

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Your examples therefore are:

I am learning Russian.
Я изучаю русский язык. (neutral, but sounds somewhat more serious)
Я учу русский язык. (tiny little bit more colloquial; leaves a tiny possibility that you don't actually want to do it).
A native speaker would say: Я изучаю русский.

I am studying at University.
Я учусь в университете.
You can't say Я изучаю университет (that means you are studying the university itself, as a bulding or an entity, its history etc).
You can't say Я изучаюсь в университете (that means you are being studied in the university, as a subject. You can be though if you have an interesting disease.)
A native speaker would say: Я учусь в университете.

I teach Russian.
Я учу русскому языку. (acceptable, but quite colloquial and may mean you do is not in a school)
Я обучаю русскому языку. (more formal, but still leaves room for interpretations)
Я преподаю русский язык. (You are a proper teacher, that is your position.)
A native speaker would say: Я преподаю русский OR Я учитель русского языка.

I teach Russian to the students.
Я учу студентов русскому языку. (colloquial)
Я преподаю студентам русский язык. (formal)
A native speaker would say: Я преподаю русский язык. (omitting "students", as it's already implied by the verb преподаю)

I teach my son how to drive a car.
Я учу сына водить машину. (that's it! No преподавать here)

I am learning to drive a car.
Я учусь водить машину. (neutral, doesn't make you sound formal)
Я изучаю вождение [машины]. (quite formal, you won't hear that in the streets)
A native speaker would say: Я учусь водить OR Я хожу на вождение.

Where did you learn Russian?
Где вы учили русский язык? (when said by a native speaker, may imply that your Russian is poor)
Где вы изучали русский язык? (neutral. No assumptions about your level in Russian).

Who taught you Russian?
Кто учил вас русскому языку? (when said by a native speaker, may imply that your teacher did a poor job)
Кто научил вас русскому языку? (this question may mean the person is surprised you know Russian)
Кто преподавал вам русский язык? (you are specifically asked for the name of the teacher)

Answer 2

I am learning Russian.

Я учу/изучаю русский язык.

I am studying at University.

Я учусь в университете.

I teach Russian.

Я преподаю русский язык.

I teach Russian to the students.

Я преподаю русский язык студентам.

I teach my son how to drive a car.

Я учу сына водить машину.

I am learning to drive a car.

Я учусь водить (машину).

Where did you learn Russian?

Где ты научился русскому языку?

Who taught you Russian?

Кто научил тебя русскому языку?

As for further examples and differences between all those words, I think quite a long essay could be dedicated to that. Let me just present some points.

• учить/преподавать

Both words mean to teach. However, when you're talking about a teacher's job/position, you use преподавать.

Я учу детей математике. I teach math to the kids. (might not be my job per se)

Я преподаю математику в школе. I teach math at school. (That's my job)

• учить/научить

Again, both words mean to teach. But the latter is perfective, meaning that it denotes completion of the teaching process.

Я учил его считать. I taught him how to count (but I don't know if he learnt)

Я научил его считать. I taught him how to count and he mastered it.

• обучать

This word is usually used with trades/skills.

Пилотов обучают с помощью тренировочных симуляторов. Pilots are trained by simulators.

• изучать

Изучать means to study, in all senses. You can closely study a problem (изучать проблему), you can study a subject (изучать предмет). When you say Я изучаю математику, it means that math is most likely one of your main subjects.

• выучить

Means to learn (completely). For example.

Я выучил это стихотворение наизусть. I learnt this poem by heart.

Я учил английский. I studies English (means the process, not the result/completion)

Я выучил английский. I learnt English ( mastered it to some degree, denotes completion)

As I said, much more can be said about these verbs. If you pick any two and ask a separate question, it would be easier to present all the differences and nuances.